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Derivative wrt one variable of an integral wrt another

  1. Mar 11, 2012 #1
    I can't seem to find this anywhere. What's
    d/dn(∫ n(w) dw)?

    That's the derivative wrt n of the integral of n over w (note: n is a function of w). Seems straightforward enough. Is there a simplification?

    Thanks
     
  2. jcsd
  3. Mar 11, 2012 #2

    mathman

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    The notation you are using to express what you want is confusing. Under the integral sign, n is a function. Outside it is a variable.
     
  4. Mar 11, 2012 #3

    HallsofIvy

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    But a function is a variable! One can always define the derivative of y with respect to a function, f(x)- dy/dx= (dy/df)(df/dx) so dy/df= (dy/dx)/(df/dx).

    So [itex]d/df \int f(x)dx= (d(\int f(x)dx)/dx)(df/dx)= f(x)(dy/dx)[/itex].
     
  5. Mar 12, 2012 #4

    mathman

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    Where did y come from?
     
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